Have I proved that time travel is impossibile?

Question

Take the equation for velocity. Velocity is a vector, meaning it is based on magnitude and direction.

Velocity = Change in Distance / Change in Time

Cross multiply to get:

Velocity * Change in Time = Change in Distance

Divide by Velocity to get:

Change in Time = Change in Distance / Velocity

Now, we want time to go backwards, so let's make the Change in Time negative. But to do so, we'll have to multiply the other side by -1 as well.

-Change in Time = -Change in Distance / Velocity

So what this is saying, is that to make time go back, we'll need to have a velocity in one direction while the distance changed from this velocity is in the other direction. This is an impossible feat.

Please tell me if there is something wrong with my logic here. I know that time travel is illogical anyway, but please tell me if I've done something wrong here.

I argue that time is not man made.

The equations we use are not man-made either. They were discovered by man, not made by man. We did not design how things worked. We discovered that we could use these equations to measure how things work! If Time is man-made, then so must speed, acceleration, force, gravity, and everything else that has time in its equation. (Which in Physics, almost everything has time in its equation, if you extend the equations to include only fundamental quantitites).

Answer 1

You're using Newtonian formulas to calculate for time travel. The formula you are using assumes that distance and time are frames of reference. That is, they never change. A mile is a mile, no matter who measures it, how is measured or when it is measured. Time is also always the same, two people starting a stopwatch at the same time will reach the minute mark at the same time, regardless of any circumstances that the "measurers" are subjected to.

Relativity dictates that space-time is the constant and that distance, and time are relative to each other. Thus, it MAKES a difference who or how you measure something and two people measuring time in different circumstances (say one stationary and the other moving at a very fast speed) will get different results.
Therefore, the formula you are using does not serve the purpose you seek. What you have proven is that to undo the distance traveled in time "t" at speed "v" would take you exactly "t" again.

Answer 2

your fallacy is with time. That equation works for the time we measure with a stop watch, but not the overall idea of time. Time is man-made, so it will work in man-made equations. But the time we think of in time travel is not the same concept of time we measure. Those are two totally different things.